Finite Group Databasebeta

← #11867140

Subgroups — #11867140

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63798C211yesmaximal, characteristic, complemented
2C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3#10594632C211yesmaximal, characteristic, complemented
4#10594612C211yesmaximal, characteristic, complemented
5#10592560C211yesmaximal, characteristic, complemented
6C3×#4865C211yesmaximal, characteristic, complemented
7C3×#4864C211yesmaximal, characteristic, complemented
8#10590833C211yesmaximal, characteristic, complemented
9#10590831C211yesmaximal, characteristic, complemented
10#10590612C211yesmaximal, characteristic, complemented
11#10590594C211yesmaximal, characteristic, complemented
12#10590515C211yesmaximal, characteristic, complemented
13#10590504C211yesmaximal, characteristic, complemented
14#10590501C211yesmaximal, characteristic, complemented
15#10590499C211yesmaximal, characteristic, complemented
16#80864—31nomaximal
17#80657—31nomaximal
18C2×#3802—21no—
19C2×#3802C2211yescharacteristic
20C2×C4×D32C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C2×#3743C2211yescharacteristic
23#64101C2211yescharacteristic
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic, complemented
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
28C2×C3×D3×C8C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#895C2211yescharacteristic
32C3×#895C2211yescharacteristic, complemented
33#63922—21no—
34#63921—21no—
35#63908C2211yescharacteristic
36#63908C2211yescharacteristic
37#63908C2211yescharacteristic, complemented
38#63902—21no—
39#63898—21no—
40#63885—21no—
41#63885—21no—
42#63856C2211yescharacteristic, complemented
43#63854—21no—
44C2×#3715C2211yescharacteristic, complemented
45C2×#3713C2211yescharacteristic, complemented
46C2×#3712C2211yescharacteristic
47C2×#3711C2211yescharacteristic, complemented
48C2×D3×C3⋊C8C2211yescharacteristic, complemented
49#63798—24no—
50D3×ΓL(1,𝔽25)—24no—
51C32×#106C2211yescharacteristic, complemented
52#63645C2211yescharacteristic, complemented
53#63635C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#911—31no—
65C2×D3×M16—31no—
66C22×ΓL(1,𝔽25)—31no—
67#5627—31no—
68#5606—31no—
69D3×#121—31no—
70D3×#121—31no—
71C3×#469—31no—
72C3×#465—31no—
73#5174—31no—
74#5157—31no—
75#5134—31no—
76#5115—31no—
77#5048—31no—
78#5042—31no—
79#5039—31no—
80#5038—31no—
81#4865D311yescharacteristic, complemented
82#4864D311yescharacteristic, complemented
83#4861—31no—
84#4861—31no—
85#4861—61no—
86#4812—31no—
87#4803—31no—
88#4782—31no—
89#4778—31no—
90#4775—31no—
91#4771—31no—
92#4770—31no—
93#4770—31no—
94C22×D32—21no—
95C22×D32D411yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#625—21no—
109C2×#625—21no—
110C2×#625—21no—
111C2×#625—21no—
112C2×#624D411yescharacteristic
113C2×D3×Dic3—21no—
114C2×D3×Dic3D411yescharacteristic
115C2×D3×Dic3D411yescharacteristic
116#3802—22no—
117#3802—22no—
118#3802—44no—
119C4×D32—22no—
120C4×D32—22no—
121#3796—22no—
122#3796—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130C4×C3⋊Dic3—21no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3743D414yescomplemented
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3—21no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D24—22no—
141C3×#204—22no—
142C3×ΓL(1,𝔽25)—22no—
143C3×D3×C8—22no—
144#3724—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3715—22no—
150#3713—22no—
151#3712—22no—
152#3711—22no—
153D3×C3⋊C8—22no—
154#3055—91noSylow
155C2×#239—31no—
156C2×#237—31no—
157C2×D3×D4—31no—
158C2×D3×D4—31no—
159C2×D3×D4—61no—
160C2×D3×D4—61no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C2×C3×SD16—31no—
164C2×C3×D8—31no—
165C2×C3×M16—31no—
166C22×C3×C8—31no—
167C3×C22⋊Q8—31no—
168C3×#121—31no—
169C3×#121—31no—
170C3×#121—31no—
171#946—31no—
172C2×#215—31no—
173#939—61no—
174#939—61no—
175#938—31no—
176#938—31no—
177#938—31no—
178#937—61no—
179D4×Dic3—61no—
180C2×#214—31no—
181C2×#213—31no—
182C2×#213—31no—
183#930—31no—
184#930—31no—
185#930—31no—
186#924—31no—
187C2×#208—31no—
188C22×C3⋊C8—31no—
189#914—64no—
190#911—64no—
191D3×M16—64no—
192C2×D24C2×D311yescharacteristic, complemented
193C2×#204C2×D311yescharacteristic, complemented
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—31no—
198C2×ΓL(1,𝔽25)—31no—
199C2×ΓL(1,𝔽25)—61no—
200C2×ΓL(1,𝔽25)—64no—
201C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
202C2×D3×C8—31no—
203C2×D3×C8C2×D311yescharacteristic, complemented
204#897C2×D311yescharacteristic, complemented
205#895C2×D311yescharacteristic
206#895C2×D311yescharacteristic
207#895C2×D311yescharacteristic, complemented
208#894—61no—
209#893—61no—
210#892—31no—
211#892—31no—
212#892—61no—
213D3×C4⋊C4—31no—
214D3×C4⋊C4—31no—
215D3×C4⋊C4—61no—
216#884—61no—
217#884—61no—
218#883—61no—
219#882—61no—
220#67⋊C4—61no—
221#67⋊C4—61no—
222D3×C22⋊C4—61no—
223D3×C22⋊C4—61no—
224C3×#106—21no—
225C3×#106C2×D311yescharacteristic, complemented
226C3×#106C2×D311yescharacteristic, complemented
227C3×#103—31no—
228C3×#102—31no—
229C3×#102—31no—
230C3×#102—31no—
231#835—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#818—31no—
239#818—31no—
240#818—61no—
241#816—31no—
242#810C2×D311yescharacteristic, complemented
243#809C2×D311yescharacteristic, complemented
244#809C2×D311yescharacteristic, complemented
245#809C2×D311yescharacteristic, complemented
246#808—31no—
247#808—31no—
248#808—61no—
249#807—31no—
250#807—31no—
251#807—61no—
252C22×C3⋊D3C2×D411yescharacteristic
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—22no—
259C2×D32—22no—
260C2×D32—41no—
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4×C3⋊D3—42no—
271C4×C3⋊D3C2×D412yes—
272C4×C3⋊D3#4112yes—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—42no—
283C3×D12—42no—
284C3×D12—42no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#625—42no—
293#625—42no—
294#625—42no—
295#625—42no—
296#624—22no—
297D3×Dic3—22no—
298D3×Dic3—22no—
299D3×Dic3—42no—
300C32×C8C2×D412yescomplemented
301C3⋊(C3⋊C8)C2×D412yescomplemented
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C2×AGL(1,ℤ/8)—91no—
305C22×M16—91no—
306#525—91no—
307C2×#121—91no—
308#469—31no—
309#469—91no—
310#468—91no—
311#468—91no—
312#466—91no—
313#466—91no—
314#465—31no—
315#465—91no—
316#428—91no—
317#418—91no—
318#417—91no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×Q8—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—61no—
344#239—62no—
345#239—62no—
346#237—62no—
347#237—62no—
348D3×D4—62no—
349D3×D4—62no—
350D3×D4—62no—
351D3×D4—62no—
352D3×D4—124no—
353D3×D4—124no—
354C2×D12—21no—
355C2×D12—21no—
356C2×D12—21no—
357C2×D12—61no—
358C2×D12C22×D311yescharacteristic
359C2×D12C22×D311yescharacteristic
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—31no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—61no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—121no—
376C2×C4×D3C22×D311yescharacteristic
377C2×C4×D3C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×SD16—62no—
380C3×D8—62no—
381C3×M16—62no—
382C2×C3×C8—21no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8—62no—
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C3×C4⋊C4—21no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#215—62no—
404#214—62no—
405#213—62no—
406#213—62no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—121no—
418C4⋊Dic3—21no—
419C4⋊Dic3—31no—
420C4⋊Dic3—31no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—121no—
430C4×Dic3—61no—
431C4×Dic3—61no—
432C4×Dic3—121no—
433#208—62no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—61no—
437C2×C3⋊C8—62no—
438C2×C3⋊C8C22×D311yescharacteristic
439C2×C3⋊C8C22×D311yescharacteristic
440D24—22no—
441#204—22no—
442ΓL(1,𝔽25)—22no—
443ΓL(1,𝔽25)—34no—
444ΓL(1,𝔽25)—34no—
445ΓL(1,𝔽25)—64no—
446ΓL(1,𝔽25)—62no—
447ΓL(1,𝔽25)—62no—
448ΓL(1,𝔽25)—62no—
449D3×C8—22no—
450D3×C8—62no—
451C22×C32C22×D411yescharacteristic
452C2×C3⋊D3—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3#12112yes—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3AGL(1,ℤ/8)12yescomplemented
470D32—44no—
471D32—84no—
472C32×C4—41no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4C2×#4111yescharacteristic
476C3⋊Dic3—41no—
477C3⋊Dic3—41no—
478C3⋊Dic3#12112yes—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C2×#41—91no—
483C22×D4—91no—
484C22×D4—181no—
485C23×C4—91no—
486AGL(1,ℤ/8)—184no—
487C2×SD16—31no—
488C2×SD16—91no—
489C2×D8—31no—
490C2×D8—91no—
491C2×M16—31no—
492C2×M16—91no—
493C2×M16—91no—
494C2×M16—91no—
495C2×M16—184no—
496C22×C8—31no—
497C22×C8—91no—
498#123—181no—
499C22⋊Q8—31no—
500C22⋊Q8—91no—
501#121—31no—
502#121—31no—
503#121—31no—
504#121—91no—
505#121—91no—
506#121—91no—
507#121—181no—
508#121—181no—
509#120—181no—
510C4×D4—181no—
511C4×D4—181no—
512#117—91no—
513C2×C4⋊C4—91no—
514C2×C22⋊C4—181no—
515#107—91no—
516#107—91no—
517#106—91no—
518#106D3211yescharacteristic, complemented
519#103—31no—
520#103—91no—
521#102—31no—
522#102—31no—
523#102—31no—
524#102—91no—
525#102—91no—
526#102—91no—
527C23×C3—31no—
528C23×C3—31no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—61no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—121no—
543C22×D3—121no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3D3×D411yescharacteristic
551C22×D3D3×D411yescharacteristic
552C3×Q8—61no—
553C3×Q8—61no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—122no—
561C3×D4—122no—
562C3×D4—122no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—31no—
569C2×C3×C4—31no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579#67—122no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—122no—
584#67—122no—
585#67—122no—
586#67—122no—
587#67—122no—
588C2×Dic3—21no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—61no—
592C2×Dic3—62no—
593C2×Dic3—62no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—122no—
601C2×Dic3D3×D411yescharacteristic
602C2×Dic3D3×D411yescharacteristic
603D12—21no—
604D12—21no—
605D12—21no—
606D12—21no—
607D12—21no—
608D12—21no—
609D12—42no—
610D12—42no—
611D12—42no—
612D12—122no—
613C4×D3—21no—
614C4×D3—21no—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—32no—
618C4×D3—32no—
619C4×D3—32no—
620C4×D3—32no—
621C4×D3—62no—
622C4×D3—62no—
623C4×D3—62no—
624C4×D3—62no—
625C4×D3—62no—
626C4×D3—62no—
627C4×D3—122no—
628C4×D3—122no—
629C4×D3—122no—
630C4×D3—242no—
631Dic6—21no—
632Dic6—21no—
633C3×C8—22no—
634C3×C8—61no—
635C3×C8—61no—
636C3×C8D3×D412yescomplemented
637C3×C8D3×D412yescomplemented
638C3⋊C8—21no—
639C3⋊C8—21no—
640C3⋊C8—32no—
641C3⋊C8—32no—
642C3⋊C8—62no—
643C2×C32C2×#12111yescharacteristic
644C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
645C2×C32#57511yescharacteristic
646C3⋊D3—22no—
647C3×D3—22no—
648C3×D3—41no—
649C3×D3—81no—
650C3×D3—81no—
651C3×D3—81no—
652C24—91no—
653C24—181no—
654#41—182no—
655#41—182no—
656C2×Q8—31no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—181no—
664C2×D4—182no—
665C2×D4—182no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—364no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—91no—
676C22×C4—91no—
677C22×C4—181no—
678C22×C4—182no—
679C22×C4—182no—
680C22×C4—181no—
681SD16—62no—
682SD16—182no—
683D8—62no—
684D8—182no—
685M16—62no—
686M16—94no—
687M16—182no—
688M16—182no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—62no—
692C2×C8—91no—
693C2×C8—182no—
694C2×C8C2×D3211yescharacteristic
695C4⋊C4—61no—
696C4⋊C4—91no—
697C4⋊C4—91no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4C2×D3211yescharacteristic
701C4⋊C4C2×D3211yescharacteristic
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—181no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C2×D3×D411yescharacteristic
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—32no—
736C2×D3—32no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—62no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—61no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—124no—
754C2×D3—124no—
755C2×D3—244no—
756C2×D3—244no—
757C2×D3#91412yescomplemented
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—81no—
767C3×C4—81no—
768C3×C4—121no—
769C3×C4C2×D3×D411yescharacteristic
770C3×C4C2×D3×D411yescharacteristic
771C3×C4D3×#4111yescharacteristic
772C3×C4D3×#4111yescharacteristic
773Dic3—21no—
774Dic3—21no—
775Dic3—32no—
776Dic3—32no—
777Dic3—41no—
778Dic3—62no—
779Dic3—121no—
780Dic3—121no—
781Dic3—121no—
782Dic3—121no—
783Dic3—241no—
784Dic3—241no—
785C32#305511yescharacteristic, complemented, Sylow
786C23—31no—
787C23—31no—
788C23—61no—
789C23—61no—
790C23—61no—
791C23—91no—
792C23—182no—
793C23—182no—
794C23—361no—
795C23—362no—
796C23—362no—
797C23—362no—
798Q8—61no—
799Q8—61no—
800D4—61no—
801D4—61no—
802D4—61no—
803D4—61no—
804D4—61no—
805D4—61no—
806D4—122no—
807D4—122no—
808D4—122no—
809D4—362no—
810D4—362no—
811D4—362no—
812D4—362no—
813D4—362no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—31no—
817C2×C4—31no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—91no—
824C2×C4—92no—
825C2×C4—92no—
826C2×C4—182no—
827C2×C4—182no—
828C2×C4—182no—
829C2×C4—181no—
830C2×C4—181no—
831C2×C4—362no—
832C2×C4—362no—
833C2×C4C22×D3211yescharacteristic
834C8—61no—
835C8—61no—
836C8—92no—
837C8#380212yescomplemented
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—62no—
842C2×C3—121no—
843C2×C3—241no—
844C2×C3—241no—
845C2×C3—241no—
846C2×C3D3×#12111yescharacteristic
847C2×C3D3×#12111yescharacteristic
848C2×C3C2×#91411yescharacteristic
849C2×C3#576811yescharacteristic
850C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
851C2×C3#577311yescharacteristic
852D3—22no—
853D3—41no—
854D3—62no—
855D3—62no—
856D3—81no—
857D3—81no—
858D3—81no—
859D3—122no—
860C22—32no—
861C22—61no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—92no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—181no—
877C22—181no—
878C22—364no—
879C22—724no—
880C22D32×D411yescharacteristic
881C4—41no—
882C4—41no—
883C4—61no—
884C4—61no—
885C4—92no—
886C4—121no—
887C4—361no—
888C4—361no—
889C4C2×#380211yescharacteristic
890C4#6431911yescharacteristic
891C3—21no—
892C3#8065711yescharacteristic, complemented
893C3#8086411yescharacteristic, complemented
894C2—62no—
895C2—121no—
896C2—182no—
897C2—241no—
898C2—241no—
899C2—241no—
900C2#1059461211yescharacteristic
901C2D3×#91411yescharacteristic
902C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#63798C2semidirect
2. C2×D3×ΓL(1,𝔽25)C2semidirect
3. #10594632C2semidirect
4. #10594612C2semidirect
5. #10592560C2semidirect
6. C3×#4865C2semidirect
7. C3×#4864C2semidirect
8. #10590833C2semidirect
9. #10590831C2semidirect
10. #10590612C2semidirect
11. #10590594C2semidirect
12. #10590515C2semidirect
13. #10590504C2semidirect
14. #10590501C2semidirect
15. #10590499C2semidirect
25. C2×C3×D24C22semidirect
26. C2×C3×#204C22semidirect
27. C2×C3×ΓL(1,𝔽25)C22semidirect
28. C2×C3×D3×C8C22semidirect
29. C3×#897C22semidirect
32. C3×#895C22semidirect
37. #63908C22semidirect
42. #63856C22semidirect
44. C2×#3715C22semidirect
45. C2×#3713C22semidirect
47. C2×#3711C22semidirect
48. C2×D3×C3⋊C8C22semidirect
51. C32×#106C22semidirect
52. #63645C22semidirect
53. #63635C22semidirect
54. #63634C22semidirect
55. C3×#810C22semidirect
56. C3×#809C22semidirect
57. C3×#809C22semidirect
58. C3×#809C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63563C22semidirect
81. #4865D3semidirect
82. #4864D3semidirect
132. #3743D4semidirect
192. C2×D24C2×D3semidirect
193. C2×#204C2×D3semidirect
201. C2×ΓL(1,𝔽25)C2×D3semidirect
203. C2×D3×C8C2×D3semidirect
204. #897C2×D3semidirect
207. #895C2×D3semidirect
225. C3×#106C2×D3semidirect
226. C3×#106C2×D3semidirect
242. #810C2×D3semidirect
243. #809C2×D3semidirect
244. #809C2×D3semidirect
245. #809C2×D3semidirect
300. C32×C8C2×D4semidirect
301. C3⋊(C3⋊C8)C2×D4semidirect
469. C2×C3×D3AGL(1,ℤ/8)semidirect
518. #106D32semidirect
636. C3×C8D3×D4semidirect
637. C3×C8D3×D4semidirect
757. C2×D3#914semidirect
785. C32#3055semidirect
837. C8#3802semidirect
892. C3#80657semidirect
893. C3#80864semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#637982
C2×D3×ΓL(1,𝔽25)2
#105946322
#105946122
#105925602
C3×#48652
C3×#48642
#105908332
#105908312
#105906122
#105905942
#105905152
#105905042
#105905012
#105904992
#808643
#806573